But say we define Mw to be a TM that on input x, erases x and emulates M on w which are constants, if the length of M's encoding is greater than |x|+20, does it mean Mw reaches position |x|+20 for any input?

In order to erase x you first have to read it entirely.
Then, you need to simulate M on w. Even if M's encoding is very short, the simulation itself may take up many cells.
On the other hand, M's simulation on w may require only few cells.